Discrete Random Variables Practice

Front

What is a discrete random variable?

Back

A discrete random variable is a type of variable that can take on a countable number of distinct values, often representing counts or whole numbers.

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on an infinite number of values within a given range, often representing measurements.

Front

What is a probability distribution?

Back

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Front

What are the properties of a valid probability distribution?

Back

1. All probabilities must be between 0 and 1. 2. The sum of all probabilities must equal 1.

Front

How do you determine if a set of probabilities is a valid probability distribution?

Back

Check if all probabilities are between 0 and 1 and if their sum equals 1.

Front

What is the probability of getting heads at least once when flipping a fair coin three times?

Back

7/8

Front

If P(X=5) = 0.11, what does this represent?

Back

This represents the probability of the random variable X taking the value of 5.

Front

What is the expected value of a discrete random variable?

Back

The expected value is the long-term average or mean of all possible values of the random variable, weighted by their probabilities.

Front

How do you calculate the expected value of a discrete random variable?

Back

Multiply each possible value by its probability and sum all these products.

Front

What is variance in the context of random variables?

Back

Variance measures the spread of a set of values, indicating how much the values differ from the expected value.